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Groups with chain Conditions on subnormal subgroups have been investigated by many authors. In this paper we give a necessarily and sufficient conditions under which a group G satisfy the ascending or the descending chain conditions on subnormal subgroups.
In this paper we prove; If R is a left quasi-Noetherian ring ,then every nil subring is nilpotent). Next we show that a commutative semi-prime quasi-Noetherian ring is Noetherian. Then we study the relationship between left Quasi-Noetherian and left Quasi-Artinian, in particular we prove that If R is a non-nilpotent left Quasi-Artinian ring. Then any left… (More)